Download 2-1-2-2rgr

OTCQ
True or False
1. An Equiangular triangle is always
equilateral.
2. An Equiangular triangle is never an
isoceles triangle.
3. A scalene triangle can be a right triangle.
OTCQ
True or False
1. An Equiangular triangle is always equilateral.
TRUE
2. An Equiangular triangle is never an isoceles
triangle.
FALSE
Isosceles means at least 2 sides/angles congruent.
1. A scalene triangle can be a right triangle.
True. Scalene means no sides angles congruent.
◦
◦
◦
A 30 - 60 – 90
right triangle would be scalene.
Aims 2-1 and 2-2
How do we define the rules of
logic? (part 1)
NY GG 24 & GG 25
Hwk read 2-1 and 2-2.
Problems 13 -20 on page 47. Do
not rewrite questions.
Objectives:
1. SWBAT think/reason with logic.
2. SWBAT define terms in logic and
apply logic rules in their arguments.
Definitions:
Inductive reasoning:
the method of thinking/reasoning from a series
of observed examples to a
conclusion/conjecture.
Example:
Observation: Ali hits 10 free throws in a row.
Conclusion/conjecture:
Ali never misses a free throw.
Definitions continued:
Counterexample: an observation that proves
that an inductive conclusion/conjecture is
false.
Example:
Observation: Ali misses next shot
Conclusion/conjecture:
Ali never misses a free throw.
PROVED FALSE!
Definitions:
Deductive reasoning:
the method of thinking/reasoning from assumptions,
definitions and general statements accepted by all as
true to a conditional statement.
Example:
Assumption#1:
Barney is a dog.
Assumption #2
All dogs bark.
Conditional Statement: If Barney is a dog,
then Barney barks.
Conditional Statement:
A statement that matches the form
“If (definition/assumption/premise),
then (conjecture/conclusion).”
Abbreviated:
Or said
p
q
p then q
Ex: If Barney is a dog, then Barney barks.
p
q
Converse of a Conditional Statement:
A conditional statement may have its p and q
switch places.
Original
p
q
Converse:
q
p
Or said
q then p
original: If Barney is a dog, then Barney barks.
Converse: If Barney barks, then Barney is a dog.
q
p
Inverse of a Conditional Statement:
A conditional statement may have its p and q negated
with the word “not”, or the words “it is not the case
that.”
Original
p
q
~p
Inverse:
~q
Or said
not p then
not q
Original : If Barney is a dog, then Barney barks.
Inverse 2 forms:
It is not the case that if Barney is a dog, then Barney
barks.
If Barney is not a dog, then Barney does not bark.
~p
~q
Contrapositive of a Conditional Statement:
A conditional statement may have its p and q negated
and switch places.
Original
p
q
Contrapositive:
~q
~q
~p
~p
Or said
then
Original: If Barney is a dog, then Barney barks.
Contrapositive:
If Barney does not bark, then Barney is not a dog.
~q
~p
Summary of part 1.
Inductive Reasoning: from observed examples to
conjectures.
Counterexamples: one example that disproves an
inductive conjecture.
Deductive reasoning: from assumed truths to
conjectures.
Conditional statements:
Basic: If (premise), then (conclusion): p
Converse:
q
Inverse:
~p
Contrapositive:
~q
q
p
~q
~p
Consider Inductive Example:
Observation: It rained all week.
Conclusion: It always rains.
Can you disprove with a
counterexample?
Sometimes you must rewrite a
conditional statement to put it in “ifthen” form
Ex:
“All Zebras have stripes.”
May be rewritten as:
“If an animal is a Zebra then it has
stripes.”
You try: rewrite the below conditional
statement to put it in “if-then” form
“Vertical angles are congruent”
You try: rewrite a conditional
statement to put it in “if-then” form
“Vertical angles are congruent”
Is rewritten as
“If two angles are vertical then they
are congruent.”
Regents
Regents
Regents: The original statement and the
contrapositive are logically equivalent.
Regents. Time permitting start
homework.
Hwk read 2-1 and 2-2.
Problems 13 -20 on
page 47. Do not
rewrite questions.